I've never used mine with an air bed, but I have inflated a paddling pool with it. You have to have the car running for it to work, so you won't run down the battery.
Mine was £16 in the auto section in Wilkinsons and is essentially a pump for inflating your car / bike tyres, like this, which seemingly has 3 adapters so may do the same thing only cheaper. It has adapters with it so you can inflate air beds / inflatable toys and footballs. It doesn't have a plug to work inthe house though, not sure if you'd get one because I guess there'd be a difference in voltage between those plug in air bed inflators you can get and the car based ones.